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joi, 27 septembrie 2012

The characteristic straight line of a trajectory


Given some spatial curve which can be traversed by a mobile, curve called trajectory, it can be shown using the recurrence theorem of the Frenet formulas that any such trajectories can be associated with a caracteristic straight line, with a single direction in space. We call this straight line associated to a trajectory just caracteristic straight line of this trajectory.

For example, the right helix caracteristic straight line is just his axis. The caracteristic straight line of the curve of constant precession (ie a 2 order helix) is the axis of the helix around which is wrapped the curve of constant precession. In the first case, we say that the caracteristic straight line has order 1, while in the second case we say that the caracteristic straight line has order 2. In general, if the trajectory is a helix of n order, then her caracteristic straight line is of order n.

Now the question arises about physical significance that has this caracteristic straight line. If any path we can associate a unique right direction, what physical meaning is that line? Does the existence of this straight line is a banal and already exploited or should make us seriously think twice from now on?

Note: this is an approximate translation obtained with the great help of the Google Translate of the previous material from Romanian.

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